The determinant of the linear transformation (matrix) T is the signed volume of the region gotten by applying T to the unit cube. (Don’t worry too much if you don’t know what the “signed” part …

Nov 27, 2019 · The determinant of the linear transformation determined by the matrix is $0$. The free coefficient in the characteristic polynomial of the matrix is $0$. Depending on the …

Elementary row operations change the determinant. They do so in a predictable way so you can keep track, but you definitely can't just put it in REF first and then find the determinant and …

I always got taught that if the determinant of a matrix is 0 0 then the matrix isn't invertible, but why is that? My flawed attempt at understanding things: This approaches the subject from a …

Mar 6, 2016 · Hints: Use $0$'s to cut down on the work. Also, you can add a multiple of one row to another row without changing the determinant. For example, here, you could start with $ …

Oct 5, 2016 · How to find the determinant of a 5x5 matrix Ask Question Asked 9 years, 2 months ago Modified 4 years, 6 months ago

Sep 29, 2015 · If determinant of a matrix is zero, it means that area of the parallelogram in the transformed space is zero. Means if you apply the matrix which has determinant zero, it will …

May 7, 2017 · For a 4x4 matrix, you expand across the first column by co-factors, then take the determinant of the resulting 3x3 matrices as above. Again, if you know Cramers Rule, you can …

Oct 13, 2017 · For a $3\times3$ determinant, symmetric or not, there is the fairly simple rule of Sarrus, but there is nothing as simple for larger determinants.

Since this last is a triangular matrix its determinant is the product of the elements in its main diagonal, and we know that in this diagonal appear the eigenvalues of $\;A\;$ so we're done.